Thank you. This router should be a good candidate for an experiment.
You do not need an Internet connection for this. When you say cellular, I assume that you can access the Internet using the iPhone (mobile broadband), but that will not be affected by the printing test. The intention is to establish a private/local Wi-Fi network (merely for AirPrint printing) using the Netgear router.
Do you have access to a computer? This may simplify the router setup.
You would not have to configure anything related to the Internet on the router. The Internet/Wide Area Network (WAN) port of the router will be left unconnected.
You would (manually) set up a Wi-Fi network and choose the appropriate wireless security, according to the instructions for the router.
See, for example, the applicable sections here:
https://www.downloads.netgear.com/files/GDC/WNR3500LV1/WNR3500L_IGPM_Combo_04Aug09.pdf
https://www.downloads.netgear.com/files/GDC/WNR3500LV1/WNR3500L_SM_11JUN2010.pdf
When a Wi-Fi network has been established, you would connect the wireless devices (printer and iPhone) to this new network.
When everything is ready, power cycle the router, the printer, and the iPhone. Try to print a document or picture already on the iPhone.
Use AirPrint to print from your iPhone or iPad - Apple Support
If you use the mobile (cellular) Internet service on the Phone to download a web page, and you want to print this, keep the page open, and then try to use AirPrint via the local Wi-Fi network. This is an experiment, so make a note of any error messages.
Good luck! Do not hesitate to post back in case of any questions. Please report your results.